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Physical Review A

Traveling-wave solutions of the Maxwell-Bloch equations

J. N. Elgin, J. B. Molina Garza

Published May 1, 1987• 15 citations
Publisher

Abstract

A possible class of traveling-wave solutions to the Maxwell-Bloch equations is presented and discussed. These are given by periodic solutions of the Lorenz equations; in particular, solutions for negative values of the parameter \ensuremath{\sigma} give stable traveling-wave solutions with phase velocity less than the speed of light.
DOI
10.1103/physreva.35.3986

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The matrix exponent method which we applied recently for the solution of the Bloch equations [Sov. Phys. JETP 62, 1125 (1985)] allows us to obtain in the present paper the Bloch-equation solutions when the amplitude and the phase of the exciting field are arbitrary functions of time. The solution's validity conditions are derived. It is shown that one can also apply the matrix exponent method to the solution of the Maxwell-Bloch equations. The equation describing the evolution of the area of a pulse with modulated envelope and phase is obtained. This equation has an analytic solution which is a generalization of the well-known McCall-Hahn solution.
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